Average Error: 58.0 → 0.0
Time: 19.6s
Precision: 64
\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
↓
\[\tanh x\]
\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}
↓
\tanh x
double f(double x) {
        double r31915 = x;
        double r31916 = exp(r31915);
        double r31917 = -r31915;
        double r31918 = exp(r31917);
        double r31919 = r31916 - r31918;
        double r31920 = r31916 + r31918;
        double r31921 = r31919 / r31920;
        return r31921;
}
↓
double f(double x) {
        double r31922 = x;
        double r31923 = tanh(r31922);
        return r31923;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.0

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  2. Using strategy rm

  3. Applied tanh-undef0.0

    \[\leadsto \color{blue}{\tanh x}\]

  4. Final simplification0.0

    \[\leadsto \tanh x\]

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))